© 2016. Published by The Company of Biologists Ltd | Journal of Experimental Biology (2016) 219, 3738-3749 doi:10.1242/jeb.143339

RESEARCH ARTICLE Accuracy of mandibular force profiles for bite force estimation and feeding behavior reconstruction in extant and extinct carnivorans François Therrien1,2,*, Annie Quinney2, Kohei Tanaka2 and Darla K. Zelenitsky2

ABSTRACT processing food. Various biomechanical approaches have been Mandibular force profiles apply the principles of beam theory to developed to investigate and compare the feeding behaviors and bite identify mandibular biomechanical properties that reflect the bite capabilities of extant and extinct mammalian predators, such as force and feeding strategies of extant and extinct predators. While beam theory (e.g. Biknevicius and Ruff, 1992a; Therrien, 2005a,b; this method uses the external dimensions of the mandibular corpus to Organ et al., 2006), jaw musculature reconstructions (e.g. determine its biomechanical properties, more accurate results could Christiansen and Adolfssen, 2005; Wroe et al., 2005; Christiansen potentially be obtained by quantifying its internal cortical bone and Wroe, 2007), and finite-element analysis (FEA) (e.g. McHenry distribution. To test this possibility, mandibular force profiles were et al., 2007; Slater et al., 2009, 2010; Tseng and Binder, 2010; calculated using both external mandibular dimensions (‘solid Tseng and Wang, 2010; Tseng et al., 2011; Jones et al., 2013; mandible model’) and quantification of internal bone distribution of Tseng, 2013; Wroe et al., 2013; Figueirido et al., 2014). Although the mandibular corpus obtained from computed tomography scans most methods require exquisitely preserved specimens (i.e. (‘hollow mandible model’) for five carnivorans (Canis lupus, Crocuta complete or undistorted specimens) and/or extensive crocuta, Panthera leo, Neofelis nebulosa and the extinct Canis dirus). computational facilities [i.e. access to computed tomography (CT) Comparison reveals that the solid model slightly overestimates scanners and bioengineering software], the mandibular force profile mandibular biomechanical properties, but the pattern of change in method is simpler and has the advantages of being easily biomechanical properties along the mandible remains the same. As reproducible, widely applicable to various taxa and requiring only such, feeding behavior reconstructions are consistent between the access to isolated mandibles (e.g. Therrien, 2005a,b; Therrien et al., two models and are not improved by computed tomography. Bite 2005; Christiansen, 2007; Blanco et al., 2011; Jasinski, 2011). force estimates produced by the two models are similar, except in C. Mandibular force profiles apply beam theory to determine the crocuta, where the solid model underestimates bite force by 10–14%. biomechanical properties of mandibles, which reflect the loads and This discrepancy is due to the more solid nature of the C. crocuta stresses endured by mandibles during life (Biknevicius and Ruff, mandible relative to other carnivorans. Therefore, computed 1992a; Therrien, 2005a,b; Therrien et al., 2005). This approach tomography improves bite force estimation accuracy for taxa with follows the assumption that bone has evolved to achieve maximum thicker mandibular corpora, but not significantly so otherwise. Bite strength with a minimum amount of material and to remodel itself in force estimates derived from mandibular force profiles are far closer to response to the loads to which it is subjected. Reflecting this notion, empirically measured bite force than those inferred from jaw both cortical thickness and bone shape will reflect the habitual loads musculature dimension. Consequently, bite force estimates derived experienced during life: elliptical shapes characterize bones that from this method can be used to calibrate finite-element analysis undergo higher bending stresses in one direction over another models. whereas greater cortical thickness characterizes bones subjected to high loads (see Wainwright et al., 1982; Lanyon and Rubin, 1985). KEY WORDS: Beam theory, Mandible, Feeding behavior, Bite force, Mandibular force profiles use the external dimensions of mandibles Carnivora, Computed tomography to model them as solid, elliptical beams composed of cortical bone that undergo bending loads during ingestion, here termed the ‘solid INTRODUCTION mandible model’ (Fig. 1; equivalent to the ‘solid symmetrical Feeding behavior and bite force are significant aspects of the model’ of Biknevicius and Ruff, 1992b). However, mandibles ecology of a predator, as both play an important role in determining modeled as solid ellipses may poorly reflect the mandible capacity the type and/or size of prey hunted and the trophic position of the to withstand bending stresses for three reasons: (1) the mandibular predator (Meers, 2002; Verwaijen et al., 2002; Wroe et al., 2005; corpus contains porous cancellous bone, thus making it partly Van Valkenburgh, 2007; see also Wiersma, 2001). Feeding hollow, (2) the amount of cancellous bone in the mandibular cross- behavior in extinct predators is usually inferred from the study of section varies along the mandible and between taxa, and (3) the their craniomandibular characteristics and dental morphology, cross-section of a mandible may differ from a perfect elliptical shape which can be interpreted as adaptations for capturing prey and (see Biknevicius and Ruff, 1992b). As such, these divergences could lead to erroneous estimation of the biomechanical properties of the mandible, resulting in the misinterpretation of feeding 1Royal Tyrrell Museum of Palaeontology, PO Box 7500, Drumheller, Alberta, behavior and bite force. Canada T0J 0Y0. 2Department of Geoscience, University of Calgary, 2500 University Drive NW, Calgary, Alberta, Canada T2N 1N4. More accurate determination of mandibular biomechanical properties can potentially be achieved by quantifying the amount *Author for correspondence ([email protected]) and distribution of cortical bone in the cross-section of the F.T., 0000-0002-2652-908X mandibular corpus through the use of X-ray imagery and CT scans (Biknevicius and Ruff, 1992b). To investigate the impact of

Received 23 May 2016; Accepted 8 September 2016 X-ray imagery on the accuracy of mandibular force profiles, Journal of Experimental Biology

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scanner (slice thickness 1 mm, pixel dimension 0.2 mm, energy List of symbols and abbreviations and current levels were not recorded but presumably close to the CA cortical bone area in mandibular cross-section standards of 120 kV and 200 mA; see Ridgely and Witmer, 2006) FEA finite-element analysis in the Department of Anthropology at the National Museum of Ix second moment of area about the mediolateral axis Natural History, Washington, DC, USA. The ramus was oriented in Iy second moment of area about the dorsoventral axis life position and CT scans were selectively made at each individual M first molar (carnassial) 1 interdental gap in the coronal plane, perpendicular to the neutral M2 second molar M3 third molar axis (which is approximated by the central axis) of the mandible P2 second premolar (Fig. 2). At the canine, CT scans were taken diagonally from the P3 third premolar lingual aspect of the symphysis through the posterior margin of P4 fourth premolar the canine alveolus so the CT slices were taken perpendicular to the TA total area of mandibular cross-section neutral axis of the mandible. The distance between each interdental USNM United States National Museum of Natural History, L Smithsonian Institution, Washington, DC gap and the middle of the articular condyle ( ) was measured with

Zx section modulus about the mediolateral axis calipers. Zx/L dorsoventral mandibular force Individual CT slices were saved as IMA files and analyzed using Zx/Zy relative mandibular force (or overall mandibular shape) the software ImageJ v. 1.40g (National Institutes of Health, Zy section modulus about the dorsoventral axis Bethesda, MD, USA). Mandibular depth and width, defined as the greatest diameter of the mandibular corpus in the vertical and horizontal planes, respectively, were measured on each CT slice mandibles of extant and extinct carnivorans were CT scanned to with the ImageJ measuring tool (Fig. 1). A few CT slices were quantify the internal distribution of cortical bone in the mandibular edited in ImageJ to better define the extent of cortical bone (with corpus in order to derive revised mandibular force profiles, an white paintbrush tool), erase cancellous bone and tooth crowns approach here termed the ‘hollow mandible model’ (Fig. 1). These (with black paintbrush tool), and fill tooth alveoli for analytical results were compared with mandibular force profiles derived from purposes (with white paintbrush tool). When the distinction external mandibular dimensions measured on the same CT data (i.e. between cortical bone and medullary cavity was difficult to ‘solid mandible model’) in order to determine: (1) whether feeding behavior interpretations differ between the two models, and (2) L whether the hollow mandible model provides more accurate bite force estimates than the solid mandible model. As such, this study will determine whether the use of CT significantly affects paleoecological interpretations based on mandibular force profiles derived from external measurements.

MATERIALS AND METHODS Samples Dentaries of five carnivoran species [Panthera leo (Linnaeus 1758), Neofelis nebulosa (Griffith 1821), Crocuta crocuta P P Canine Canis lupus Post-M P3P4 2 3 (Erxleben 1777), Linnaeus 1758 and the extinct 3 M2M3 M M P4M1 Canis dirus Leidy 1858], each represented by two large adult 1 2 specimens (Table 1), were scanned on a Siemens Somatom CT

Post-M3 M1M2 P4M1 P3P4 Canine P2P3 M2M3

Fig. 1. Use of computed tomography (CT) scans to calculate the biomechanical properties of carnivoran mandibles. (A) Raw CT slice. Fig. 2. Orientation of CT slices taken at interdental gaps along the (B) Alteration of CT slice to remove cancellous bone/tooth crown and fill cortical mandible. The mandibular ramus was oriented in life position and CT scans bone/tooth alveolus to determine biomechanical properties following the were taken at each interdental gap in the coronal plane, perpendicular to the hollow mandible model. (C) External linear measurements of mandibular central axis of the mandible. At the canine, CT scans were taken diagonally corpus used to determine biomechanical properties following the solid from the lingual aspect of the symphysis through the posterior margin of the mandible model. The CT slice illustrated is the M2M3 interdental gap of Canis canine alveolus. Distance of each interdental gap to the articular condyle (L) dirus (USNM 8305). was also measured (double-headed arrows). Journal of Experimental Biology

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Table 1. Mandibular dimensions and biomechanical properties of carnivorans Solid model Hollow model

3 3 3 3 2 2 Specimen/interdental gap Depth (cm) Width (cm) L (cm) Zx (cm ) Zy (cm ) Zx (cm ) Zy (cm ) CA (cm ) TA (cm ) Canis dirus (USNM 8305, jaw length=19.23 cm)

Post-M3 4.68 1.82 5.85 3.91 1.52 3.58 1.29 4.83 6.65 M2M3 4.34 1.84 6.75 3.40 1.44 2.98 1.37 4.40 6.17 M1M2 4.07 1.84 7.7 2.99 1.35 2.72 1.37 5.00 6.12 P4M1 3.89 2.13 11.06 3.16 1.73 2.39 1.36 4.20 6.02 P3P4 3.43 2.03 12.65 2.34 1.39 1.80 1.03 3.76 4.92 P2P3 3.41 2.09 – 2.39 1.46 1.70 0.92 3.43 4.76 Canine 3.64 3.53 16.86 4.59 4.45 3.58 3.42 8.23 8.34 Canis dirus (USNM 8307, jaw length=21.1 cm)

Post-M3 4.56 1.84 6.03 3.76 1.52 3.20 1.22 4.85 5.97 M2M3 4.45 1.86 6.6 3.62 1.51 2.95 1.07 4.36 5.70 M1M2 4.07 1.86 7.88 3.02 1.38 2.75 1.14 5.18 5.65 P4M1 3.8 1.95 11.4 2.76 1.42 2.19 1.25 4.60 5.63 P3P4 3.28 1.8 13.34 1.90 1.04 1.44 0.79 3.28 4.31 P2P3 3.12 1.72 – 1.64 0.91 1.37 0.69 3.01 3.93 Canine 3.16 2.88 18 2.82 2.57 2.28 1.90 6.07 6.07 Canis lupus (USNM 274487, jaw length=20.2 cm)

Post-M3 4.21 1.22 6.31 2.12 0.62 1.92 0.53 2.75 4.05 M2M3 4.14 1.22 6.91 2.05 0.60 1.93 0.49 2.72 4.01 M1M2 3.95 1.3 8.3 1.99 0.66 1.89 0.64 3.44 4.25 P4M1 3.91 1.75 11.05 2.63 1.18 2.07 0.88 3.61 4.93 P3P4 3.34 1.64 13.05 1.80 0.88 1.43 0.67 2.78 3.89 P2P3 2.99 1.46 – 1.28 0.63 1.01 0.52 2.57 3.19 Canine 3.18 2.72 17.68 2.70 2.31 1.82 1.63 5.13 5.50 Canis lupus (USNM 274942, jaw length=est. 19.7 cm)

Post-M3 4.07 1.57 5.87 2.55 0.98 2.00 0.72 2.91 4.80 M2M3 3.97 1.59 6.61 2.46 0.99 1.87 0.63 2.70 4.59 M1M2 3.74 1.61 7.64 2.21 0.95 1.66 0.77 3.45 4.67 P4M1 3.38 1.89 10.73 2.12 1.19 1.85 1.06 4.12 4.87 P3P4 2.91 1.74 12.54 1.45 0.86 1.22 0.75 2.83 3.76 P2P3 2.74 1.68 – 1.24 0.76 0.95 0.61 2.81 3.24 Canine 2.87 2.79 17.1 2.26 2.19 1.69 1.58 5.18 5.26 Crocuta crocuta (USNM 368502, jaw length=18.5 cm)

Post-M1 5.31 1.4 5.75 3.88 1.02 3.71 0.74 4.61 5.36 P4M1 4.51 1.78 8.83 3.55 1.40 2.88 0.89 4.53 5.44 P3P4 4.14 1.84 11.1 3.10 1.38 2.74 1.21 5.19 5.82 P2P3 4.14 2.16 14 3.63 1.90 2.87 1.75 5.11 6.83 Canine 3.86 2.64 15.8 3.86 2.64 3.07 2.11 6.88 6.93 Crocuta crocuta (USNM 181524, jaw length=18.43 cm)

Post-M1 4.82 1.32 6.3 3.01 0.82 3.00 0.76 4.25 4.91 P4M1 3.86 1.53 9.35 2.24 0.89 2.21 0.84 4.21 4.68 P3P4 3.32 1.7 11.38 1.84 0.94 1.74 0.92 4.25 4.40 P2P3 3.43 2.06 14.5 2.38 1.43 1.72 1.23 4.08 5.08 Canine 3.45 2.34 15.95 2.73 1.85 2.14 1.49 5.46 5.49 Neofelis nebulosa (USNM 49974, jaw length=12.10 cm)

Post-M1 2.24 0.99 4.98 0.49 0.22 0.48 0.19 1.34 1.76 P4M1 2.22 1.18 6.37 0.57 0.30 0.48 0.26 1.77 2.01 P3P4 2.33 1.12 7.81 0.60 0.29 0.57 0.29 1.90 2.09 P2P3 2.51 1.14 – 0.71 0.32 0.57 0.26 1.55 2.23 Canine 2.83 1.66 10.55 1.31 0.77 1.29 0.75 3.65 3.72 Neofelis nebulosa (USNM 196600, jaw length=10.96 cm)

Post-M1 1.99 0.89 4.5 0.35 0.15 0.34 0.14 1.16 1.40 P4M1 1.89 0.99 6.04 0.35 0.18 0.34 0.18 1.43 1.52 P3P4 1.93 1.01 7.46 0.37 0.19 0.32 0.16 1.32 1.45 P2P3 2.04 0.97 – 0.40 0.19 0.34 0.17 1.13 1.59 Canine 2.39 1.45 9.58 0.81 0.49 0.87 0.55 2.83 2.85 Continued Journal of Experimental Biology

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Table 1. Continued Solid model Hollow model

3 3 3 3 2 2 Specimen/interdental gap Depth (cm) Width (cm) L (cm) Zx (cm ) Zy (cm ) Zx (cm ) Zy (cm ) CA (cm ) TA (cm ) Panthera leo (USNM 162913, jaw length=est. 22.7 cm)

Post-M1 5.6 2.29 10.8 7.05 2.88 5.79 1.84 6.81 9.57 P4M1 5.02 2.27 13.5 5.62 2.54 4.45 2.21 6.31 8.81 P3P4 4.43 2.23 16.1 4.30 2.16 3.51 2.03 6.36 7.62 P2P3 4.47 2.14 – 4.20 2.01 3.14 1.69 4.89 7.35 Canine 5.31 3.65 21.2 10.10 6.95 7.45 5.35 12.41 12.79 Panthera leo (USNM 181569, jaw length=21.97 cm)

Post-M1 5.12 2.02 10.06 5.20 2.05 4.61 1.28 5.66 7.70 P4M1 4.69 2.06 12.99 4.45 1.95 3.53 1.84 5.49 8.03 P3P4 4.33 2.12 15.32 3.90 1.91 3.12 1.89 6.05 7.20 P2P3 4.23 2.15 – 3.78 1.92 2.67 1.66 4.33 7.22 Canine 4.96 3.38 19.48 8.16 5.56 5.88 4.24 10.51 11.23 L is the distance separating the articular condyle from the specified interdental gap. Jaw length was estimated for two specimens based on comparison with the conspecific individual. Section moduli (Z) for the ‘solid mandible model’ were calculated from the depth and width of the mandibular corpus measured on CT slices. Section moduli for the ‘hollow mandible model’, cortical area (CA) and total area (TA) were calculated with the MomentMacro in ImageJ. USNM, United States National Museum of Natural History, Smithsonian Institution, Washington, DC.

determine in a CT slice, comparison with the CT slice for the same the second moment of area determined by MomentMacro. (2) Zy, interdental gap in the second individual of the same species was the section modulus or maximum bending strength about the made in order to delineate the extent of the cortical bone. dorsoventral axis: for the solid ellipse model, Zy=π×(mandibular Biomechanical properties (see below), total surface area (TA) of depth/2)×(mandibular width/2)2/4 and for the hollow mandible the mandibular corpus cross-section, and surface area represented model, Zy=Iy/(mandibular width/2), where Iy is the second moment by cortical bone (CA) in the mandibular corpus cross-section were of area determined by MomentMacro. (3) Zx/L, the dorsoventral quantified in each CT slice using the MomentMacro version 1.3 mandibular force. By assuming constancy of bone material property (freely available at http://www.hopkinsmedicine.org/FAE/mmacro. and safety factor in the vertebrate mandible, the flexure formula of htm) run within ImageJ. Timoshenko and Gere (1972) can be modified to show that the applied force on a structure can be expressed as the ratio of the Mandibular force profiles section modulus over the moment arm length (for details, see Following the principles of beam theory, mandibles can be Therrien, 2005a). As such, Zx/L is a measure of the maximum force modeled as cantilevers undergoing bending loads during food applied in the dorsoventral plane at an interdental gap, where L is the ingestion (for reviews of the methodology and equations, see distance separating the interdental gap studied from the articular Therrien, 2005a; Therrien et al., 2005). Biomechanical properties condyle. (4) Zx/Zy, the relative mandibular force (or overall of the mandible are calculated based on the dimensions of the mandibular shape) at a given point. (5) CA/TA, the ratio of mandibular corpus and the distribution of cortical bone within it cortical bone area to total surface area of the mandibular corpus (Biewener, 1992; Biknevicius and Ruff, 1992a). In this study, the cross-section; a measure of the ‘hollowness’ of the mandible at a second moment of area (I), a measure of bone distribution around a given interdental gap. given axis, is evaluated in two different ways: (1) using Species means were calculated for each of the aforementioned measurements of the vertical (i.e. dorsoventral) and horizontal variables. For the hollow mandible model, species means were (i.e. labiolingual) diameters of the mandibular corpus, which calculated from the values produced by MomentMacro. For the assumes that the latter has a solid elliptical cross-section (sensu the solid mandible model, linear measurements (mandibular depth, solid mandible model, see Fig. 1); and (2) through quantification mandibular width, and distance to interdental gaps) of both (via the MomentMacro) of cortical bone distribution in the individuals of a given species were averaged prior to calculating the mandibular corpus based on CT scan images, which takes into mandibular biomechanical properties. The graphic representation of consideration the actual shape of the mandibular corpus cross- variations in biomechanical properties, namely, bending force (Z/L) section (i.e. any deviation from a perfect elliptical cross-section) and relative mandibular force (Zx/Zy), along the mandible are called and the presence of cancellous bone in the corpus (sensu the mandibular force profiles and have been shown to reflect differences hollow mandible model, see Fig. 1). Because the hollow mandible in feeding behavior among predators (Therrien, 2005a,b; Therrien model takes into consideration the actual shape of and the internal et al., 2005; Christiansen, 2007; Blanco et al., 2011; Jasinski, 2011). distribution of cortical bone in the mandibular corpus, its results are considered to represent the true biomechanical properties of the Bite force estimation mandible (see Biknevicius and Ruff, 1992b). Following the approach of Therrien (2005a), Zx/L values at the From the second moment of area, the following properties were carnassial (P4M1 and M1M2 or post-M1 in felids and C. crocuta), evaluated for both solid and hollow mandible models at each where maximum bite force is theoretically achieved in carnivorans interdental gap. (1) Zx, the section modulus or maximum bending (Greaves, 1983, 1985), were used as a bite force proxy for each strength about the mediolateral axis: for the solid ellipse model, taxon. The Zx/L values of each taxon were compared with those of P. 2 Zx=π×(mandibular width/2)×(mandibular depth/2) /4 and for the leo, providing a ‘relative bite force’ estimate expressed as a percent hollow mandible model, Zx=Ix/(mandibular depth/2), where Ix is value of the bite force of the lion (Table 2). Journal of Experimental Biology

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To assess the accuracy of bite force estimates derived from mandibular force profiles, values were compared with bite force estimates derived from measurements of cross-sectional areas and ‘ ’ (49%) (108%) lever arms of major jaw adductor muscles (the dry skull method of a b Thomason, 1991) and empirical in vivo bite force measurements Experimentally determined bite force 4500 (Table 2). Because the bite force values from the various methods could only be compared if expressed in relative terms (i.e. relative to the lion bite force), we limited our search to studies that evaluated both the bite force of P. leo and of other taxa considered in our study – – in order to insure consistency of methodology and bite force estimates. Empirically measured bite forces, reported in absolute Thomason (1991) corrected bite force 1412.2 (34%) 2000 4167.6 (100%) terms (i.e. Newtons), were expressed relative to Thomason’s (1991) bite force estimate for P. leo. Although an empirically derived bite force for the lion would have been preferable, this estimation method has been considered a reliable proxy in felids in the absence –– of empirical data (Sakamoto et al., 2010). Christiansen and Wroe (2007) 773.9 (38%) corrected 1711.2 985.5 (49%) corrected 2177 2023.7 (100%) corrected 4462.9 544.3 (27%) corrected 1205.7 Statistical analyses To compare the degree of hollowness of the various carnivoran mandibles, the CA/TA ratios at post-canine interdental gaps were compared for all specimens by performing a one-way ANOVA with post hoc tests for multiple comparison on samples where equal variance is not assumed using the software IBM SPSS Statistics 22.0. corrected 3461.8 Wroe et al. (2005, supplementary data) 1033 (33%) corrected 2281.7 1577 (51%) corrected 3479.4 1569 (51%) 3085 (100%) corrected 6800 1051 (34%) corrected 2321.3 RESULTS Comparison of solid and hollow mandible models

– Comparison via bivariate plots reveals that the solid and hollow mandible models follow similar trends but differ in absolute values, the magnitude of difference varying between species and as a Christiansen and Adolfsen (2005) corrected 2786.5 corrected 3137.2 corrected 7505 corrected 1301.5 function of the location along the mandible. The solid mandible model generally overestimates the true biomechanical properties (as expressed by the hollow mandible

solid Carn. (N) Carn. (N) Carn. (N) Carn. (N)model) Carn. (N) of mandibular strength (Zx; Fig. 3) and mandibular force 1

M Z L ). For the bite force derived from the jaw musculature method, both published values and corrected values (if not published) are

4 ( x/ ; Fig. 4). Posterior to P3P4, the solid mandible model Therrien (2005b) overestimates Zx and Zx/L in canids and P. leo (by 10–31%), but significantly less so in C. crocuta and N. nebulosa (<12%). At P2P3, the solid ellipse model overestimates Zx by approximately 30% in Panthera leo

solid P canids and C. crocuta, 37% in P. leo, and 17% in N. nebulosa. 1 M

4 (Because the distance from the articular condyle to P2P3 was only available for C. crocuta, Zx/L values could only be calculated for this species and are overestimated by 29% by the solid ellipse Z solid P model.) At the canine, the solid mandible model overestimates x 1 and Zx/L in all carnivorans (by 25–41%), except N. nebulosa, where these values are slightly underestimated (by 4%). In estimating the relative mandibular force (Zx/Zy), the solid ellipse model generally provides values close to those of the hollow (present study) L / Zx Zy

x mandible model (Fig. 5). Among canids, the / values produced Z hollow Post-M by the two models are usually within 10% of each other, although 1 M

4 the solid model consistently underestimates the values in the post- carnassial region. This underestimation of Zx/Zy values in the post- carnassial region is due to the fact that Zy values are overestimated

hollow P to a greater extent (proportionally speaking) than Zx values by the 1 solid model (see Table 1). In C. crocuta, the Zx/Zy values produced by the two models are within 17% of each other and nearly identical 0.22 (45%) 0.18 (60%) 0.26 (45%) 0.22 (58%) 0.17 (50%) 1262.3 (37%) 0.35 (70%) 0.20 (68%) 0.39 (66%) 0.26 (70%) 0.22 (64%) 0.56 (112%) 0.28 (93%)0.50 (100%) 0.30 0.57 (100%) (98%)0.09 (17%) 0.58 (100%) 0.31 (83%) 0.07 (22%) 0.38 (100%) 0.35 (104%) 0.09 (15%) 0.34 (100%) 1421.6 (42%) 0.07 (19%) 3405.4 (100%) 0.06 (19%) 587.8 (17%) at P3P4 and at the canine. In N. nebulosa, the Zx/Zy values produced by the two models are nearly identical along the entire tooth row, except behind the carnassial, where the solid ellipse model stands for estimates provided at the carnassial without precision of the exact position. ’ underestimates the Zx/Zy value by 11%. The greatest divergence is P. leo Z Z Carn. observed in , where the solid ellipse model overestimates x/ y ‘ values by 5–20% along the entire tooth row, except behind the N. L. Denton, Purdue University,Binder personal and communication. Van Valkenburgh (2000; their fig. 3A). Journal of Experimental Biology Table 2. Comparison of bite force estimates produced by various methods a b Taxon Post-M Canis lupus Canis dirus listed. Values in parentheses are relative bite force (i.e. expressed relative to the bite force of Crocuta crocuta Panthera leo Neofelis nebulosa carnassial, where it underestimates values by 25%.

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Felidae Canidae Hyaenidae A 10 4 4 Panthera leo solid 9 Panthera leo hollow 8 Neofelis nebulosa solid 3 3 7 Neofelis nebulosa hollow 6

x 5 2 2 Z 4 3 1 Canis lupus solid 1 2 Canis lupus hollow 1 Canis dirus solid Crocuta crocuta solid Canis dirus hollow Crocuta crocuta hollow 0 0 0

B1.6 1.6 1.6

1.2 1.2 1.2 ,hollow x

Z 0.8 0.8 0.8 ,solid/

x 0.4 0.4 0.4 Z

Panthera leo Canis lupus Neofelis nebulosa Canis dirus Crocuta crocuta 0 0 0 Post-M1 P4M1 P3P4 P2P3 CaninePost-M3 M2M3 M1M2 P4M1 P3P4 P2P3 Canine Post-M1 P4M1 P3P4 P2P3 Canine

Fig. 3. Comparison of section modulus (Zx) values produced by the solid mandible and hollow mandible models for studied carnivorans. (A) Profiles of

Zx values along the mandible. The pattern of change in Zx along the mandible is nearly identical in the two models, but the values for the solid model slightly exceed those for the hollow model. (B) Ratios of Zx values produced by the solid mandible and hollow mandible models. The solid model slightly overestimates Zx values produced by the hollow model, generally by ∼20% (i.e. ratio close to 1.2), except in Neofelis nebulosa and Crocuta crocuta, where Zx values are more similar (i.e. ratio closer to 1.0). The solid model overestimates Zx at the canine in all carnivorans except in N. nebulosa, where it is slightly underestimated.

CA/TA ratio 99%) but differ in the posterior portion of the mandible. The The hollowness of the mandible, expressed by the CA/TA ratio, mandibles of canids and P. leo are moderately solid (CA/TA ∼73– varies along the mandible and between species (Fig. 6). All species 86%), except in the postcarnassial region of C. lupus and at P2P3 in have a nearly solid mandibular corpus at the canine (CA/TA ∼95– P. leo, where they are more hollow (CA/TA ∼63–64%). In contrast,

A Felidae Canidae Hyaenidae Panthera leo solid Canis lupus solid Crocuta crocuta solid 0.6 Panthera leo hollow Canis lupus hollow Crocuta crocuta hollow Neofelis nebulosa solid Canis dirus solid Neofelis nebulosa hollow Canis dirus hollow

0.4

L / x Z

0.2

0 B 1.6 ) L / 1.2 hollow x

Z 0.8 )/( L

0.4 solid/ x Canis lupus Z Panthera leo

( Canis dirus Crocuta crocuta 0 Neofelis nebulosa Post-M1 P4M1 P3P4 CaninePost-M3 M2M3 M1M2 P4M1 P3P4 Canine Post-M1 P4M1 P3P4 P2P3 Canine

Fig. 4. Comparison of dorsoventral mandibular force (Zx/L) values produced by the solid mandible and hollow mandible models for studied carnivorans. (A) Profile of Zx/L values along the mandible. The pattern of change in Zx/L along the mandible is nearly identical in the two models, but the values for the solid model slightly exceed those for the hollow model. (B) Ratios of Zx/L values produced by the solid and hollow mandible models. The solid model slightly overestimates Zx/L values produced by the hollow model, generally by ∼10–30% (i.e. ratio varying between 1.1 and 1.3), except in N. nebulosa and C. crocuta, where Zx/L values are more similar (i.e. ratio closer to 1.0). The solid mandible model overestimates Zx/L at the canine in all carnivorans except in N. nebulosa, where it is slightly underestimated. Journal of Experimental Biology

3743 RESEARCH ARTICLE Journal of Experimental Biology (2016) 219, 3738-3749 doi:10.1242/jeb.143339

Felidae Canidae Hyaenidae A 5 Panthera leo solid Canis lupus solid Crocuta crocuta solid Panthera leo hollow Canis lupus hollow Crocuta crocuta hollow 4 Neofelis nebulosa solid Canis dirus solid Neofelis nebulosa hollow Canis dirus hollow 3 y Z / x Z

2

1

0

B 1.4 1.2 1.0 0.8 0.6 solid/hollow y Z

/ 0.4 x Z

0.2 Panthera leo Canis lupus Neofelis nebulosa Canis dirus Crocuta crocuta 0 Post-M1 P4M1 P3P4 P2P3 CaninePost-M3 M2M3 M1M2 P4M1 P3P4 P2P3 Canine Post-M1 P4M1 P3P4 P2P3 Canine

Fig. 5. Comparison of Zx/Zy values produced by the solid mandible and hollow mandible models for studied carnivorans. (A) Profile of Zx/Zy values along the mandible. The pattern of change in Zx/Zy along the mandible is nearly identical in the two models. (B) Ratios of Zx/Zy values produced by the solid mandible and hollow mandible models. The solid mandible model generally provides values close to those of the hollow mandible model. Among canids, the two models are usually within 10% of each other, although the solid model consistently underestimates the values in the post-carnassial region. In C. crocuta, the two models are within 17% of each other and are nearly identical at P3P4 and at the canine. In N. nebulosa, the two models are nearly identical along the entire tooth row, except behind the carnassial, where the solid mandible model underestimates Zx/Zy by 11%. In Panthera leo, the solid mandible model overestimates Zx/Zy values by 5– 20% along the entire tooth row, except behind the carnassial, where it underestimates values by 25%. the mandibles of C. crocuta and N. nebulosa are generally far more when it generally overestimates Zx and Zx/L values is due to the fact solid (CA/TA ∼86–92%), except at P2P3, where they are in the range that the lion mandible is more hollow at the carnassial than that of observed among canids (70–77%). These results indicate that the other taxa, resulting in a greater discrepancy of Zx/L values between medullary cavity in the mandibles of C. crocuta and N. nebulosa is solid and hollow models in that reference taxon than in other taxa. much smaller than in other carnivorans, usually occupying only The two models differ the most in C. crocuta, where the solid 8–14% of the mandibular cross-section as opposed to 14–37% in mandible model underestimates relative bite force values by other carnivorans (see also Tseng and Binder, 2010). A statistical 10–14%. These results are largely consistent with Therrien’s comparison of CA/TA values for all post-canine interdental gaps (2005a) bite force estimates based on the solid model (Fig. 7, reveals that the mandibular corpus of C. crocuta is significantly Table 2), the slight incongruences most likely due to differences in more solid than that of C. lupus and P. leo (P<0.027) and C. dirus sample size, i.e. mean of seven individuals in Therrien (2005a) (P=0.097), but similar to that of N. nebulosa (P>0.957). versus mean of two individuals in the present study. Interestingly, relative bite force estimates calculated anterior (at P4M1) and Relative bite force estimates posterior (at M1M2 or post-M1) to the carnassial differ by 4–15%, Relative bite force estimates derived from the solid ellipse and except in C. crocuta, where the difference is much greater (15–19%). hollow mandible models are generally consistent (within 4%) among most taxa, with the solid model usually underestimating bite DISCUSSION force values produced by the hollow model (Fig. 7, Table 2). The Our study demonstrates that mandibular force profiles are a reliable reason why the solid model produces lower bite force estimates approach to document the biomechanical properties of carnivoran

Canidae Felidae and Hyaenidae Fig. 6. Comparison of CA/TA values (the 1.2 ratio of cortical bone area to total surface 1.0 area of the mandibular corpus cross- section) for studied carnivorans. The 0.8 mandibles of canids and P. leo are moderately solid (73–86%), except in the postcarnassial

0.6 region of C. lupus and at P2P3 in P. leo where ∼ CA/TA CA/TA they are more hollow ( 63%). The mandibles 0.4 of C. crocuta and N. nebulosa are generally far – 0.2 Panthera leo more solid (86 92%), except at P2P3,where Canis lupus Neofelis nebulosa they are in the range observed among canids Canis dirus Crocuta crocuta 0 (70–77%). All species have nearly solid – Post-M3 M2M3 M1M2 P4M1 P3P4 P2P3 Canine Post-M1 P4M1 P3P4 P2P3 Canine mandibles at the canine (95 99%). Journal of Experimental Biology

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Fig. 7. Comparison of bite force estimates obtained Empirically determined bite force from various methods. Each bite force estimate is Hollow model (present study) 120 reported relative to the bite force value of P. leo obtained Solid model (present study) by the same estimation method. Estimates derived from Therrien (2005a) mandibular force profiles (solid and hollow models) are Christiansen and Adolfssen (2005) 100 generally higher and closer to empirically determined bite Wroe et al. (2005) force (star) than those derived using Thomason’s (1991) Christiansen and Wroe (2007) jaw musculature method (gray symbols). Only in N. Thomason (1991) 80 nebulosa are bite force estimates derived from mandibular force profiles lower or equal to those derived from the jaw musculature method.

60

40 Relative bite force (%)

20

0

Crocuta crocutaCanis lupus Canis dirus Neofelis nebulosa mandibles and, consequently, to infer the feeding behavior and bite From an ecological and behavioral perspective, the general pattern force of extant and extinct taxa. Although the solid mandible model of change in biomechanical properties along the mandible is does not record the ‘true’ biomechanical properties of the mandible consistent between the solid and hollow models (Figs 3–5), (as represented by the hollow mandible model), the two approaches resulting in identical feeding behavior interpretations for the produce comparable results. While the solid ellipse model tends to carnivorans studied. Furthermore, the fact that the magnitude of overestimate mandibular strength (Zx) and mandibular force (Zx/L), change in biomechanical properties exceeds the aforementioned it generally closely reflects relative mandibular force (Zx/Zy). solid–hollow model discrepancy and intraspecific variation confirms Similar conclusions were reached by Biknevicius and Ruff the validity of mandibular force profile analysis for feeding behavior (1992b) in their comparison of various approaches to calculate the reconstructions. The much lower Zx/L values at the canine than at the second moment of area (I) of carnivoran mandibles. Although the carnassial seen in canids and C. crocuta reflect their pack hunting difference between the solid and hollow mandible models is not behavior, where individuals deliver numerous shallow canine bites to always consistent between interdental gaps, which could raise weaken prey (e.g. Kruuk, 1972; Ewer, 1973; Biknevicius and Ruff, concerns about the validity of the solid mandible model, this 1992a; Therrien, 2005a). The higher Zx/L values at the canine and discrepancy is generally ≤20% (see Figs 3–5). While this steeper increase in Zx/L values along the tooth row observed in the discrepancy may appear large in relative terms, its absolute extinct C. dirus presumably reflect mandibular adaptations to subdue magnitude (0.04–0.12 for Zx/L and 0.4–0.8 for Zx/Zy) is so small large Pleistocene herbivores (Therrien, 2005a; see also Anyonge and that it often falls within the range of intraspecific variation (i.e. Baker, 2006). In contrast, the high Zx/L values at the canine relative to values between two similar-sized individuals of a given species can the carnassial observed in felids reflect the powerful, canine killing differ by as much as the solid model discrepancy, see Table 1). As bite these solitary hunters deliver to subdue prey (Kruuk and Turner, such, the solid model discrepancy is minimal and does not alter the 1967; Schaller, 1972; Ewer, 1973; Therrien, 2005a). interpretation of the results. Given the primary purpose of Mandibular force profiles also provide insight into the bone- mandibular force profiles to infer feeding behavior, it is the cracking abilities of carnivorans (see Therrien, 2005a). Although relative pattern of change in biomechanical properties (primarily pre-carnassial (i.e. P4M1 and P3P4) Zx/Zy values remain constant in Zx/L and Zx/Zy ratios) along the mandible that is of relevance. The felids and canids, reflecting the fact that this region of the mandible only instances where the actual value of a biomechanical property is is used for slicing flesh, they increase posteriorly in C. crocuta. This used to infer feeding behavior are: (1) the Zx/Zy value at the canine increase in Zx/Zy values over the pre-carnassial corpus reflects a (i.e. to infer the method of prey capture) and (2) the Zx/L values at species that cracks bone with the premolars (Rensberger, 1995; Van the carnassial (i.e. to infer bite force) (see Therrien, 2005a). In the Valkenburgh, 1996). By contrast, canids crush bones with their first case, the solid and hollow models are shown to produce nearly post-carnassial molars (M1–M3; Ewer, 1973) and, in these species, identical Zx/Zy values at the canine (ratio of the two models is ∼1.0; the increase in Zx/Zy values occurs posterior to M1. The more see Fig. 5). In the second case, Zx/L values at the carnassial are anteriorly situated bone-processing location in hyaenids allows shown to be nearly identical between the solid and hollow models them to break larger bones but requires (1) relatively larger bite (see Accuracy of bite force estimates derived from mandibular force forces because of the reduced mechanical advantage induced by profiles, below). Consequently, the solid mandible model is a cracking bones at a greater distance from the jaw joint (Greaves, reliable approach to reconstruct feeding behavior. However, if one 1985) and (2) deeper mandibular corpora (i.e. posteriorly increasing seeks to determine the exact values of the biomechanical properties Zx/Zy values) to sustain stresses associated with this behavior of the mandible (e.g. to infer peak stress the mandible can (Biknevicius and Ruff, 1992a). The post-carnassial Zx/Zy values of withstand), the hollow mandible model should preferably be canids, including the extinct C. dirus, are lower than those of applied. C. crocuta, as originally noted by Therrien (2005a), which indicate Journal of Experimental Biology

3745 RESEARCH ARTICLE Journal of Experimental Biology (2016) 219, 3738-3749 doi:10.1242/jeb.143339 poorer adaptations for bone processing. Although both canids have takes into consideration cortical bone distribution and thickness in less cortical bone in their mandibular cross-section than hyaenids the mandibular cross-section. Comparison of the two models, (Fig. 6), the post-carnassial mandibular corpus of C. dirus is however, reveals that relative bite force estimates are usually close characterized by slightly thicker (9–13%) cortical bone than that of (within 4% of each other), with the greatest divergence (10–14%) C. lupus (Fig. 6), resulting in greater mandibular bending strength observed in C. crocuta. This divergence is due to the significantly (Zx) values in the extinct canid, approaching values observed in greater thickness of cortical bone in hyaenid mandibles (CA/TA C. crocuta (Fig. 3). Nevertheless, the lower Zx/Zy values produced ∼90%) relative to other carnivorans (CA/TA ∼60–85%). Thus the by hollow mandible models confirm that dire wolves were not as solid mandible models produce bite force estimates that are nearly adept bone crushers as modern gray wolves and clearly lacked the identical to the hollow mandible models, except in taxa with a thick adaptations for osteophagy of hyaenids (Van Valkenburgh and cortical bone layer in the mandibular corpus. Koepfli, 1993; Therrien, 2005a; Anyonge and Baker, 2006; contra Large differences exist between bite force estimates derived from Meehan and Martin, 2003). Indeed, extant canids are considered the hollow mandible model and those obtained from the dimension unspecialized for osteophagy (Biknevicius and Ruff, 1992a) and of the jaw adductor musculature (Fig. 7, Table 2). The least extreme tend to crush bones rather than crack them like hyaenids (Werdelin, differences are observed in N. nebulosa, where the bite force 1989). Despite having a mandible characterized by a very thick layer estimates derived from hollow mandible models are generally of cortical bone like that of C. crocuta, N. nebulosa does not display within 17% (depending on the landmark being considered) of those any biomechanical mandibular adaptations associated with based on jaw musculature dimension. In canids, the hollow osteophagy (i.e. the Zx/Zy profile remains constant over the cheek mandible model provides bite force estimates that are 7–27% teeth, indicative of a slicing function). Furthermore, its highly higher than those based on jaw adductor musculature. The greatest specialized dentition, characterized by a blade-like carnassial, differences are observed in C. crocuta, where the hollow mandible absence of postcarnassial teeth, and narrowed premolars, is model provides estimates that are 42–70% higher than those based indicative of a hypercarnivorous diet without bone-cracking on jaw adductor musculature. abilities (Holliday and Steppan, 2004). Thus the thickened Ultimately, true assessment of the accuracy of bite force estimates cortical bone layer of this felid is not an adaptation to withstand produced by mandibular force profiles requires comparison with bending stresses associated with bone cracking. Neofelis nebulosa is experimentally determined bite force values (i.e. recorded in live known for hunting prey both smaller (e.g. small primates, birds) and subjects). Despite a plethora of bite force values presented in far larger than itself (e.g. large primates, deer, wild boars), which it documentaries and blogs, experimentally determined bite force dispatches with a powerful bite to the back of the neck (see Banks, values have been published for few mammal species (Thomason 1949; Prater, 1971; Payne et al., 1985; Rabinowitz et al., 1987; et al., 1990; Dessem and Druzinsky, 1992; Ström and Holm, 1992; Grassman et al., 2005; Chiang, 2007). Thus the greater cortical bone Binder and Van Valkenburgh, 2000; Ellis et al., 2008). Of relevance thickness of the mandibular corpus in N. nebulosa may be an to our study, the highest recorded bite force for C. crocuta approaches adaptation to deliver powerful bites to capture large prey. 4500 N (Binder and Van Valkenburgh, 2000; Fig. 3A) and Interestingly, this mandibular condition is also observed in preliminary attempts to empirically determine the bite force of C. sabertoothed predators (Akersten, 1985; Biknevicius and Van lupus (Thomas et al., 2005) reveal a bite force of approximately Valkenburgh, 1996; McHenry et al., 2007), adding to the list of 2000 N (N. L. Denton, Purdue University, personal communication). convergences between N. nebulosa and these extinct predators Comparison reveals that mandibular force profiles consistently (Therrien, 2005b; Christiansen, 2005, 2008). produce bite force estimates that are far closer to the empirically Although the thickened mandibular corpus of C. crocuta measured bite force (accuracy to within 4–15% for the hollow model certainly offers a biomechanical advantage for bone cracking (see and 10–25% for the solid model) than those produced by the jaw Biknevicius and Ruff, 1992a), the question of whether this musculature method (11–16% lower in C. lupus and 57–66% lower condition represents an adaptation for osteophagy rather than a in C. crocuta) (Fig. 7, Table 2). Even after application of the phylogenetic signal has yet to be investigated. The facts that early correction factor for the disparity between dry skull and in vivo bite hyaenids were civet-like insectivores or omnivores and that force (Thomason, 1991; Sakamoto et al., 2010), absolute bite force craniodental features indicative of bone-cracking abilities did not estimates produced by the jaw musculature method are still 23–52% evolve until later (e.g. Werdelin and Solounias, 1996; Turner et al., lower than empirical bite forces for C. crocuta (also noted by Tseng 2008) suggest that thickened mandibular corpora may be an and Binder, 2010), but are slightly closer for C. lupus (ranging from adaptation for durophagy in that clade. Nevertheless, the fact that 15% lower to 39% higher than empirical values) (Fig. 7, Table 2). both N. nebulosa and the sabretooth Smilodon possess thicker These results support the long-held suspicion that Thomason’s mandibular corpora indicates that this condition also occurs in non- (1991) jaw musculature method greatly underestimates bite force osteophagous taxa. As such, the presence of a thickened mandibular (see Therrien, 2005a; Ellis et al., 2008; Davis et al., 2010). corpus may not be exclusively an adaptation for osteophagy but However, the congruence between empirically determined and rather an adaptation to sustain greater stresses associated with hollow-model-derived bite force values expressed relative to P. leo powerful bites, be it for durophagy or for subduing large prey. suggests that the jaw musculature method might produce accurate Interestingly, a thickened mandibular corpus evolved independently bite force estimates for this felid (see Sakamoto et al., 2010). The in some aquatic vertebrates as an adaptation for buoyancy or bottom poorer performance of the jaw musculature method has been feeding (Domning and Debuffrenil, 1991; Houssaye, 2009; Jones ascribed to a variety of issues, such as the fact that the method: (1) et al., 2013) and not for delivering powerful bites. does not account for interspecific variation in jaw muscle pennation, (2) assumes that muscle cross-sectional area and lever arm length Accuracy of bite force estimates derived from mandibular correlate directly with bite force, and (3) considers the mandible as a force profiles two-dimensional object only, which overestimates the cross- The hollow mandible model should theoretically provide more sectional area of the masseter and pterygoid muscles and accurate bite force estimates than the solid ellipse model because it underestimates the cross-sectional area of the temporalis muscle Journal of Experimental Biology

3746 RESEARCH ARTICLE Journal of Experimental Biology (2016) 219, 3738-3749 doi:10.1242/jeb.143339 in many carnivorans (Wroe et al., 2005; Ellis et al., 2008; Davis model) with those derived from external mandibular dimensions et al., 2010; Tseng and Binder, 2010). Thus mandibular force assuming a solid mandible (i.e. the solid mandible model) reveals profiles, particularly the hollow mandible model, are a more that the two models are highly congruent. The solid mandible model accurate and far simpler method to estimate bite force than generally overestimates biomechanical properties relative to the Thomason’s (1991) jaw musculature method. hollow mandible model, but the overall pattern of change along the Given the greater accuracy of bite force estimates derived from jaw is accurately represented. Furthermore, bite force estimates mandibular force profiles, this method can be used to infer the bite produced by the two models are highly similar to each other and to force of the extinct C. dirus and of the elusive N. nebulosa. Previous empirically determined bite force, except for the spotted hyena studies have shown that C. dirus was similar to C. lupus in terms of C. crocuta owing to the greater cortical bone thickness in the feeding behavior but, because of its overall larger size and mandibular corpus of this osteophagous taxon. Consequently, robustness, could deliver a stronger bite (see Therrien, 2005a; reconstruction of the feeding behavior and bite force for most Anyonge and Baker, 2006; Meloro et al., 2015). Supporting this carnivorans can be achieved with the solid mandible model without view, the hollow mandible model indicates that C. dirus had a bite the need for time-consuming, often limited access and costly CT. force that was 66–70% that of P. leo, which is 11–59% stronger than Only when dealing with a taxon that possesses thicker cortical bone that of C. lupus (8%–25% when expressed relative to P. leo). The within its mandibular corpus (e.g. hyaenids, sabertooths) will the hollow mandible model thus confirms that C. dirus was capable of a solid model slightly underestimate the bite force of the animal. very powerful bite, presumably an adaptation to kill large Pleistocene Thus, CT may help provide more accurate bite force estimates for prey. In comparison, the estimated bite force of N. nebulosa is these taxa by permitting documentation of the internal distribution approximately 20% that of P. leo, values that are generally lower than of cortical bone in the mandibular corpus. estimates produced by the jaw adductor musculature method, except Finally, mandibular force profiles, based on either the solid or the for one study (Fig. 7, Table 2). It is unclear why bite force estimates hollow models, are shown to produce more accurate bite force based on the jaw musculature method are generally higher in this estimates than those derived from jaw muscle architecture instance, but it does not seem to be related to the study of larger measurements on dry skulls. This discrepancy has important individuals as both methods employed individuals of similar size implications for the use of FEA, as this method often uses bite (compare table 1 in Therrien, 2005a with table 1 in Wroe et al., 2005). force estimates inferred from muscle architecture measurements to calibrate virtual models of extant and extinct taxa. Use of incorrect Implications for the calibration of finite-element analysis bite force values may affect the validity of FEA models, especially as (FEA) models it relates to predicting the bite force of extinct taxa and documenting Over the past two decades, FEA has been used extensively to stress distribution during bite. Mandibular force profiles may thus investigate the relationship between form and function in extant and provide an alternative method to obtain more accurate bite force extinct animals (for reviews, see Fastnacht et al., 2002; Rayfield, estimates for FEA in the absence of empirically determined bite force 2007; Cunningham et al., 2014). Although this non-destructive values. Furthermore, given that the feeding behaviors reconstructed approach has gained in popularity, it remains anchored in numerous from mandibular force profiles are generally consistent with those assumptions, including some about cranial and muscle architecture obtained from the FEA studies (e.g. Tseng and Binder, 2010), and the amount of force generated by the jaw musculature mandibular force profile analysis has great potential for elucidating (Fastnacht et al., 2002; Bright, 2014). While muscle architecture the ecology of extinct predators known from limited fossilized can be inferred from muscle scars and dissection of extant relatives, remains. the amount of force muscles can generate is often based, in the absence of empirically determined values, on bite force estimates Acknowledgements derived from jaw musculature reconstructions (e.g. Wroe et al., We wish to thank Bruno Frohlich (Department of Anthropology, USNM) for assistance with CT scanning, as well as Linda Gordon (Department of Vertebrate 2007; McHenry et al., 2007; Wroe, 2008; Slater et al., 2009). As Zoology, Mammals Division, USNM) and Robert Purdy and Michael Brett-Surman noted above, bite force estimates derived from such methods tend to (Department of Paleobiology, Vertebrate Paleontology Division, USNM) for access dramatically underestimate true bite force in mammalian predators. to specimens in their care. We are indebted to Nancy L. Denton (Purdue As such, although FEA can be used to document and compare stress Polytechnic Institute, Purdue University) for sharing unpublished bite force and load distributions in skulls of different morphology, use of this measurements in gray wolves and to Rachel Frigot (Johns Hopkins University, School of Medicine) for providing missing length measurements on two method to infer the bite force generated by a predator or to infer specimens. We also wish to thank Susan Virtue for her assistance in compiling stress distribution during ‘typical bite’ ought to be done with caution tables and formatting the manuscript. Finally, we are grateful to Blaire Van (Bright, 2014). While other approaches have been developed to Valkenburgh and one anonymous reviewer for their thorough review that helped produce more accurate bite force estimates in carnivorans (e.g. Wroe improve the manuscript. et al., 2008; Tseng and Wang, 2010; Tseng and Binder, 2010; Slater et al., 2010), mandibular force profiles may represent a simpler Competing interests The authors declare no competing or financial interests. alternative method to obtain accurate bite force values (after converting relative bite force estimates to absolute values) with Author contributions which FEA models can be calibrated. F.T. conceived the study. F.T. and A.Q. conducted the analyses. All authors assessed the results and wrote the manuscript. Conclusions The mandibular force profile approach provides a simple and widely Funding applicable method to investigate the feeding behaviors and bite This work was partially supported by a Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grant (327513-2009 to D.K.Z.). force of extant and extinct predators. Although the method is theoretically sensitive to the distribution of cortical bone within the Data availability mandibular corpus, comparison of results derived from the precise CT images are freely available on ResearchGate at https://www.researchgate.net/ quantification of bone distribution via CT (i.e. the hollow mandible publication/309702204_CT_scans. Journal of Experimental Biology

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